Secant and Tangent Lines

The green line always passes through the two green points.
If you drag the mouse while holding either button down on a
circle, that point will move and the corresponding curve will change
accordingly.
Clicking on "snap" will move the green points to their nearest integer
x-coordinates.
You may change the yellow curve to either a parabola, exponential or
cubic curve by clicking in the "Change to _______" box.

The green points will, with luck, always remain on the yellow curve.
If the points are different, you get a secant line to the curve through
those points.
If you move one of these points
on top of the other, then you should see a message to the right
saying what happens in this case.
For each of the three possible yellow curves, try to find a relationship
between the slope of the resulting line and the x-coordinate where the points
coincide.